Carter,
I make a great display case - looks fantastic - here's what I do.
Get a sheet of 4 or 5 mm clear perspex, and decide how large you want the case to be.
Make a base from MDF or Craftwood - you know, that stuff that's made from wood dust and resin (not chipboard). Rebate the edges with a router to just a whisker over the thickness of the perspex.
Now for the case - measure the perspex so that the finished case is the same as the outside measurements of the base - this will mean that the inside edges of the case will just clear the rebate on the base.
Cut your perspex but leave on the protective paper coating or you'll scratch it - I use a tablesaw with a 40 tooth tungsten carbide blade - the more teeth, the smoother the cut. Make sure the blade clears the thickness of the perspex by only a millimetere or two, or you'll chip the edges of the cuts.
Once you've got the sides and the top cut, peel off the protective paper and assemble the sides, then put the top on. Use a glue that's designed for perspex -I've used a Plastruct glue - can't remember which one - and it does the same with perspex that liquid glue does to styrene - melts it a little and welds the perspex together. Normal styrene glue won't touch it. Use whatever method you need to ensure the sides are square - maybe use the base as a jig.
When all the edges are glued and hardened, I chamfer all of the glued edges of the perspex with a belt sander to 45 degrees - I go down about as far as the thickness of the sheet.
This hides the glue joint and gives an overall frosty appearance to the edges and completely hides the joint. It looks great!! I've made quite a number of them, for myself and for others, and everyone loves them.
I treat the base using the spatter paint spray packs available at paint stores - they have a base color and two lighter shades in spatter paint. There are several different types like sandstone, granite, and some browns and greens. They're very effective and the finished bases look impressive. If you have any questions about my methods, just email me using the link and I'll tell you whatever you need to know to make a teriffic base for yourself.
Cheers,
Lee Tree